Torsional loads are ubiquitous during everyday dextrous manipulations. We examined how information about torque is provided to the sensorimotor control system by populations of tactile afferents. Torsional loads of different magnitudes were applied in clockwise and anticlockwise directions to a standard central site on the fingertip. Three different background levels of contact (grip) force were used. The median nerve was exposed in anaesthetized monkeys and single unit responses recorded from 66 slowly adapting type‐I (SA‐I) and 31 fast adapting type‐I (FA‐I) afferents innervating the distal segments of the fingertips. Most afferents were excited by torque but some were suppressed. Responses of the majority of both afferent types were scaled by torque magnitude applied in one or other direction, with the majority of FA‐I afferent responses and about half of SA‐I afferent responses scaled in both directions. Torque direction affected responses in both afferent types, but more so for the SA‐I afferents. Latencies of the first spike in FA‐I afferent responses depended on the parameters of the torque. We used a Parzen window classifier to assess the capacity of the SA‐I and FA‐I afferent populations to discriminate, concurrently and in real‐time, the three stimulus parameters, namely background normal force, torque magnitude and direction. Despite the potentially confounding interactions between stimulus parameters, both the SA‐I and the FA‐I populations could extract torque magnitude accurately. The FA‐I afferents signalled torque magnitude earlier than did the SA‐I afferents, but torque direction was extracted more rapidly and more accurately by the SA‐I afferent population.